Matrix representation
For the problem input into Xpress Optimizer, the mathematical model is transformed into the following constraint matrix (Table QP matrix).
| frac1 | frac2 | frac3 | frac4 | frac5 | frac6 | frac7 | frac8 | frac9 | frac10 | ||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Oper. | RHS | ||
| MinNA | 0 | 10 | 13 | 16 | 19 | ≥ | 0.5 | ||||||
| Allfrac | 1 | 11 | 14 | 17 | 110 | 112 | 114 | 116 | 118 | 120 | 122 | = | 1 |
| Yield | 2 | 52 | 175 | 268 | 1211 | 813 | 915 | 717 | 619 | 3121 | 2123 | ≥ | 9 |
| ↑ | ↑ | ||||||||||||
| rowidx | matval | ||||||||||||
| colbeg | 0 | 3 | 6 | 9 | 12 | 14 | 16 | 18 | 20 | 22 | 24 | ||
As in the previous chapters, the superscripts for the matrix coefficients indicate the order of the entries in the arrays rowidx and matval, the first three entries of which are highlighted (printed in italics).
The coefficients of the quadratic objective function are given by the following variance/covariance matrix (Table Variance/covariance matrix).
| frac1 | frac2 | frac3 | frac4 | frac5 | frac6 | frac7 | frac8 | frac9 | frac10 | ||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | ||
| frac1 | 0 | 0.1 | |||||||||
| frac2 | 1 | 19 | -2 | 4 | 1 | 1 | 1 | 0.5 | 10 | 5 | |
| frac3 | 2 | -2 | 28 | 1 | 2 | 1 | 1 | -2 | -1 | ||
| frac4 | 3 | 4 | 1 | 22 | 1 | 2 | 3 | 4 | |||
| frac5 | 4 | 1 | 2 | 4 | -1.5 | -2 | -1 | 1 | 1 | ||
| frac6 | 5 | 1 | 1 | 1 | -1.5 | 3.5 | 2 | 0.5 | 1 | 1.5 | |
| frac7 | 6 | 1 | 1 | 2 | -2 | 2 | 5 | 0.5 | 1 | 2.5 | |
| frac8 | 7 | 0.5 | -1 | 0.5 | 0.5 | 1 | 0.5 | 0.5 | |||
| frac9 | 8 | 10 | -2 | 3 | 1 | 1 | 1 | 0.5 | 25 | 8 | |
| frac10 | 9 | 5 | -1 | 4 | 1 | 1.5 | 2.5 | 0.5 | 8 | 16 |